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In the Sorcerer's Stone, Snape was playing with the Quirrell the double agent job. He was persuading him to find out how to get the stone.
"Have you found out how to get past that beast of Hagrid's yet?"
"B-b-but Severus, I --"
"You don't want me as your enemy, Quirrell," said Snape, taking a step toward him.
Harry-Potter-and-the-Philosopher's-Stone, CHAPTER THIRTEEN
But in the Quidditch match Snape
saved Harry and Quirrel knew that.
Later Harry discussed with Quirrel:
"But Snape tried to kill me!"
"No, no, no. I tried to kill you. Your friend Miss Granger accidentally knocked me over as she rushed to set fire to Snape at that Quidditch match. She broke my eye contact with you. Another few seconds and I'd have got you off that broom. I'd have managed it before then if Snape hadn't been muttering a countercurse, trying to save you."
"Snape was trying to save me?"
"Of course," said Quirrell coolly. (...)
Harry-Potter-and-the-Philosopher's-Stone, CHAPTER SEVENTEEN
How is it possible, that Voldemort trusted Snape later so much? And that nobody brought this up. (I know, it may be out of screen, but Snape's position seems pretty strong)